Özdin, Tufan

Let S = End(M) be the ring of endomorphisms of a right R-module M. In this paper we define the minus parital order for the endomorphism ring of modules. Also, we extend study of minus partial order to the endomorphism ring of a (Rickart) module. Thus, several well-known results concerning minus partial order are generalized.

Altunbaş, Murat

In this paper, we obtain explicit formulae for homogenous Ricci solitons on three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces. We also give a result about Ricci solitons on a three dimensional Minkowski space.

Özkan, Engin; Uysal, Mine

We define a new generalization of Gaussian Pell-Lucas polynomials. We call it d−Gaussian Pell-Lucas polynomials. Then we present the generating function and Binet formula for the polynomials. We give a matrix representation of d−Gaussian Pell-Lucas polynomials. Using the Riordan method, we obtain the factorizations of Pascal matrix involving the polynomials.

Işık, Fikret; Taşyurdu, Yasemin

In this paper, we consider Hessenberg matrices and Fibonacci-Like sequences that is defined by therecurrence relation Tn = Tn−1 + Tn−2, n ≥ 2 and T0 = m, T1 = m where m is a fixed positive integer. We define twon × n Hessenberg matrices with applications to the Fibonacci-Like sequences and investigate the determinantal andpermanental properties. We obtain that the determinants and permanents of these Hessenberg matrices are equal tothe nth term of Fibonacci-Like sequences.

Akpınar, Ayşe; Taşyurdu, Yasemin

In this paper, we define the Padovan and Pell-Padovan octonions by using the Padovan and PellPadovan numbers. We give the generating functions, Binet’s formulas, sums formulas and some properties forthese octonions. We also present the matrix representations of the Padovan and Pell-Padovan octonions.